In the stellar atmospheres, state of matter at different points of the plasmas is non-linearly coupled by radiation transfer. Multiple processes leave their fingerprints in polarization state of light (scattering, collisions, magnetic fields, etc.). Polarization is thus a key observable providing invaluable information on the local physical conditions. Direct inversion of the physical quantities is often mathematically ill defined but a comparison of the observations with sufficiently realistic models provides suitable quantitative diagnostics and constrains of our models. I will briefly review the processes involved in the non-LTE polarized radiative transfer problem and I will show how is the ongoing research in this field related to the present and future space experiments in solar physics.

Johanes Kepler, living in Prague, utilized observations carried out by Tycho Brahe also on the Czech territory to formulate the law known today as the “3rd Kepler law”. We recall it in its classical form and will derive it for relationship between the mean motion and selected mean semi-major axis of orbit of an artificial Earth satellite (AES) accounting for the polar flattening of the Earth. This simple tool has amazing applications in selection of orbits of AES to fulfill given tasks “at the best”. There is a close relation between density of ground tracks by satellite data, on which in turn precision and resolution of products derived from such measurements are dependent, and semi-major axis (or height of flight) of the satellite used. We tell the story of the GRACE satellites, which during their free decay in the atmosphere encountered important orbit resonances during those the density of ground tracks significantly (but temporarily) decreased. Consequently, also the quality of the monthly solutions for the variations of the gravity field has decreased. What we learned from GRACE, we applied for orbit choice of GOCE, the first satellite equipped by a gravity gradiometer. In this matter, we joined the manager of the GOCE project Dr. Rune Flobergahen, ESA. GOCE is also equipped by ultraprecise ion motor for orbit corrections so that the height of flight can be kept within unbelievably small range ±5 m. It is feasible to choose and keep the orbit at selected higher order resonance and by this way to reach the maximum quality of products derived from gradiometric measurements. This process is called „fine orbit tuning“. Orbit choice for remote sensing AES affects significantly the accuracy of the results derived from their measurements, thus our approach captured interest of ESA in the project of bistatic altimetric satellite GNSS-R. We also investigated the orbit choice for planetary orbiters of Mars, Venus and the Moon from viewpoint of possible most accurate determination of gravity field parameters of these bodies.

The fall of the bolide Benešov occurred over Central Bohemia 22 years ago, on 7 May 1991. It became one of the most important bolide ever observed and from the very beginning it was clear that this very bright event terminated by a meteorite fall. However despite great efforts and many attempts no meteorite was found in the weeks and years after the fall. In spring 2011, just before 20th anniversary of this extraordinary case, all available all-sky records were re-measured and re-analyzed. Slightly different methods and new approaches which were gradually developed for analysis of several recent instrumentally observed meteorite falls resulted in finding of a new consistent picture of the Benešov event. It explained unsuccessful search in years after the fall and suggested new strategy which could lead to recovery of Benešov meteorites after 20 years. This new scenario was completely confirmed by find of for small meteorites of corresponding masses exactly in the predicted impact area. This result is in many aspects pioneering. It was proved that in some special cases it is still possible to predict and find meteorites long time after the fall. However the most important result is in heterogeneity of the recovered meteorites. Three different types of material discovered in these meteorites clearly show that larger meteoroids can be compositionally very complicated bodies. The Chelyabinsk superbolide of February 15, 2013 was the most energetic meteoric event globally since the Tunguska explosion in 1908. The blast wave caused moderate damage (broken windows etc.) in the city of Chelyabinsk and surrounding areas and injured about 1500 people. Thanks to numerous casual video records, the superbolide was well documented. Precise positional calibration of the videos represents, however, a challenge. We will report our work in progress of determining the bolide trajectory, velocity, fragmentation and dust trail formation.

During the last decades, several studies had focused on the determination of the prominence temperatures. However, practically all of them were based on the analysis of mainly optical spectral line shapes which brings several difficulties and uncertainties, namely in cases when the spectral lines are optically thick. At the same time, the need for a reliable determination of the temperature in central coolest parts of quiescent prominences has grown as a result of new modeling efforts trying to understand the energy-balance conditions. Using the microwave spectra with a high spatial resolution offers the new possibility. We demonstrate that the fine structures in solar quiescent prominences can be well detected with the ALMA interferometer (Atacama Large Millimeter Array in Chile, joint project of ESO, USA and Japan). ALMA is going to be fully operational and a special hardware setup will allow soon the solar observations. We simulate the visibility of prominence fine structures, their brightness temperatures at various wavelengths and demonstrate the feasibility and usefulness of ALMA observations of solar prominences. Our basic approach is the conversion of high-resolution H-alpha coronagraphic images into the microwave spectral images. Finally, we apply the ALMA image-processing software CASA to our simulated images to see what the ALMA would detect in reality. We discuss various ways how to determine the prominence kinetic temperature from ALMA spectral images.

Nuclear star clusters are unambiguosly detected in about 50--70 % of spiral and spheroidal galaxies. They have typical half-light radii of 2--5 pc, dynamical mass ranging from 10^6--10^7 Msun, are brighter than globular clusters, and obey similar scaling relations with host galaxies as supermassive black holes. The Nuclear Stellar Cluster (NSC) which surrounds Sgr A*, the SMBH at the centre of our galaxy, is the nearest nuclear cluster to us, and can be resolved to scales of milliparsecs. The strong and highly variably extinction towards the Galactic centre makes it very hard to infer the intrinsic properties of the NSC (structure and size). We attempt a new way to infer its properties by using Spitzer MIR images in a wavelength regime (3--8 microns) where the extinction is at a minimum, and the NSC clearly stands out as a separate structure. We present results from our analysis, including extinction-corrected images and surface brightness profiles of the central few hundred parsecs of the Milky Way.

The ability to automatically find spectra of given properties in large data set could be vital for many reasons in astronomy. Discovering rare phenomena (like emission stars) or finding objects with extreme features as an example. Automation is also crucial because of dramatic increase of data volume produced by modern surveys such as SDSS and LAMOST. Tools and techniques of data acquisition, pre-processing and classification are discussed. Suggested methods are demonstrated on Ondrejov 2m telescope archive and Sloan Digital Sky Survey (SDSS).

Determination of binary and precessing asteroid shapes and rotation parameters from inversion of their light curves have reached interesting applications in last years. Two recent results will be presented: 1. Photometric observations of binary Near-Earth asteroid 1996 FG3 taken from 1996 to 2013 lead to a solution for a quadratic drift of the mean anomaly of the mutual orbit close to zero value. This result confirms a recent theory of binary YORP (BYORP) effect where asymetric emission of thermal radiation and mutual tides between the two components are taken into account. 2. An inversion of a shape and a rotation state of a precessing asteroid (99942) Apophis will be presented. The outcome of Apophis modeling will be important for its Earth-impact probability refining in future, including the YORP and Yarkovski effects.